Question

The Magazine Mass Marketing Company has received 14 entries in its latest sweepstakes. They know that the probability of receiving a magazine subscription order with an entry form is 0.4 . What is the probability that no more than 3 of the entry forms will include an order? Round your answer to four decimal places.

Answer 1

P=0.1238.

Explanation:

We know that the Magazine Mass Marketing Company has received 14 entries in its latest sweepstakes. They know that the probability of receiving a magazine subscription order with an entry form is 0.4 .

We calculate the probability that no more than 3 of the entry forms will include an order.

We know that n=14, p=0.4 and q=0.6. We get

`P(X=0)=C_0^(14)\cdot 0.4^0\cdot 0.6^(14)=0.00028\\\\P(X=1)=C_1^(14)\cdot 0.4^1\cdot 0.6^(13)=0.00731\\\\P(X=2)=C_2^(14)\cdot 0.4^2\cdot 0.6^(12)=0.03169\\\\P(X=3)=C_3^(14)\cdot 0.4^3\cdot 0.6^(11)=0.08451\\`

Therefore, the probability is

P=0.00028+0.00731+0.03169+0.08451

P=0.12379

P=0.1238.